Problem-Solving and Data Analysis
| English | 中文 | Pinyin |
|---|---|---|
| median/ˈmiːdiːən/ | 中位数 | zhōng wèi shù |
| random sample/ˈrændəm ˈsæmpl/ | 随机样本 | suí jī yàng běn |
A decision before an answer
- A 20% discount followed by a 20% increase does not return a price to its starting point.
- Your goal: Use ratios, rates and percentages.
Read the relationship
- Percent change uses the original value as the denominator. Percentage points compare percentages directly.
- Interpret distributions and compare centre and spread.
For 2,3,4,5,100 the median is:
The third of five ordered values is 4.
Use the defining rule
- Convert units explicitly. A rate denominator describes the amount of time or distance used.
- Calculate probabilities and assess sample claims.
A bag has 3 red and 5 blue counters. P(red)?
There are 8 equally likely counters, 3 red.
Check the conditions
- The median resists extreme values more than the mean. Spread describes variation, not the average.
- Calculate probabilities and assess sample claims.
A price of 80 falls by 20%: 80×0.8=64. It then rises by 20%: 64×1.2=76.8. The final value is below 80 because the two percentage changes use different bases.
A rise from 40 to 50 is a ____% increase.
The increase is 10 divided by the original 40.
Apply the task format
- A random sample supports generalisation to its sampling population. Random assignment concerns causal comparison, a different issue.
- Calculate probabilities and assess sample claims.
A sample from volunteers is not automatically representative, even when it is large.
Which answer fits this case?
Use ratios, rates and percentages
Random sampling and random assignment serve exactly the same purpose.
Sampling supports generalisation; assignment helps causal comparisons.
Keep the distinctions
- median 中位数 — The middle value in an ordered data set.
- random sample 随机样本 — A sample selected using a chance process.
- Use ratios, rates and percentages.
- Interpret distributions and compare centre and spread.
- Calculate probabilities and assess sample claims.
Match each term with its precise meaning in this lesson.
Keep the distinctions stated in the teaching example.
Put this lesson’s reasoning or event sequence in order.
The order follows the stated process; check each stage before the next.